Imaging optical system

ABSTRACT

A luminous flux, from one conjugate surface (A), having an opening angle of at least 10° sequentially passes through a first optical system ( 30 ) having a luminous flux convergent action in the vicinity of its reference axis and a second optical system ( 31 ) having a luminous flux divergent action in the vicinity of its reference axis, and converges on another conjugate surface (B). A specific condition is given to the converging distance of each converging point at a luminous flux section including a principal ray according to the passing position of the luminous flux through the first optical system ( 30 ) to thereby implement an oblique-incident optical system having a half angle of at least 60° and a comparatively simple structure irrespective of a type of an optical element used.

TECHNICAL FIELD

[0001] The present invention relates to an imaging optical systemcapable of reading an image from an oblique direction and of projectingan image.

BACKGROUND ART

[0002] Imaging optical systems relating to oblique image reading orimage projection (hereinafter referred to simply as “oblique-incidenceimaging optical systems”) are classified into oblique-incidence imagingoptical systems of a decenter system and oblique-incidence image-formingoptical systems of a tilt system.

[0003]FIG. 24 illustrates the basic principle of the oblique-incidenceimaging optical system of the decenter system. In this oblique-incidenceimaging optical system of the decenter system, an object plane 4 andimage plane 2, which are conjugate planes, are basically parallel toeach other, and the optical axis 3A of an image-forming optical system30 is perpendicular to both the object plane 4 and the image plane 2. Torealize an oblique-incidence imaging optical system, for example, animage detecting region 201 included in the image plane 2 is shiftedbelow the optical axis 3A. Consequently, an image pick-up region 401included in the object plane 4 is shifted upward as viewed in FIG. 24and a oblique-incidence image-forming optical system can be realizedwithout using any special optical system. The decenter system isadvantageous in that any excessive distortion does not occur. However,the same system is disadvantageous in that the image circle of theimage-forming optical system 30 must be large to displace the opticalaxis 3A, the correction of aberration is difficult and the imagingoptical system 30 is large.

[0004]FIG. 25 illustrates the basic principle of the tilt system. Thetilt system differs greatly from the decenter system in that the opticalaxis 3A of an imaging optical system 30 is oblique to an object plane 4,and an image plane 2 is oblique to the optical axis 3A. Respectiveprolongations of the image plane 2, the object plane 4 and the principalplane of the imaging optical system 30 intersect on a line A ofintersection to meet Scheimpflug's principle, i.e., an imaging conditionfor the tilt system. The tilt system is advantageous in that the imagingoptical system 30 is not excessively large and resolving power iscomparatively high. The same system is disadvantageous in that a newdistortion occurs. FIG. 26 shows a typical example of such a distortion,which can be readily understood from the examination of imagingmagnification illustrated in FIG. 25. oblique-incidence imaging opticalsystems are classified into those of the decenter system, those of thetilt system and those of a composite system having the characteristicsof both the decenter and the tilt system. The image-forming opticalsystem must meet predetermined conditions about particulars includingresolving power and distortion required of the optical system. Variousdevices have been proposed to solve problems in those systems andefforts have been made to provide optical systems answering purposes.Some examples of prior art optical system will be described.

[0005]FIG. 27 shows a projection lens for a projector disclosed in JP-ANo. Hei 05-273460 in a sectional view. A projection lens 30 consistingof refracting optical elements, and an image-forming device 2 are movedperpendicularly to the optical axis 3A of the projection lens 30relative to each other to realize an oblique-incidence imaging opticalsystem. To avoid moving a condenser lens 301 disposed near theimage-forming device 2, the optical axis of the projection lens 30 istilted when moving the projection lens 30. Therefore, it is consideredthat this oblique-incidence imaging optical system is basically of thedecenter system and uses tilting for the degree of freedom ofcorrection. This optical system achieves image projection in a maximumfield angle 2ω of about 510.

[0006]FIG. 28 shows a projector disclosed in U.S. Pat. No. 5,871,266 tothe applicant of the present invention patent application in a sectionalview. The projector includes, as essential components, an illuminatingsystem 1 including a light source, an image-forming device 2 including aliquid-crystal display or the like, and an imaging system 3. Theilluminating system 1 and the imaging system 3 are optimized to realizean oblique-incidence imaging optical system. In a concrete example, theimaging system 3 comprises only a small number of reflecting mirrors. Alight beam emitted by the illuminating unit 1 is decomposed into lightbeams of three primary colors by dichroic mirrors 2 a and 2 b toilluminate three reflecting image-forming devices 2 g, 2 h and 2 i.Light beams reflected by the reflecting image-forming devices 2 g, 2 hand 2 i are combined by the dichroic mirrors 2 a and 2 b, and the lightbeams travel toward the imaging system 3. The imaging system 3 has threereflecting mirrors 3 a, 3 b and 3 d. The light beams from the reflectingimage-forming devices 2 g, 2 h and 2 i are reflected by the reflectingmirrors 3 a, 3 b and 3 d to form an image on a screen 4, not shown. Inthis specification, the significance of the oblique-incidence imagingoptical system included in the projector is discussed minutely. Anexample applied to a thin rear projection display capable of achievingimage projection in a maximum field angle 2ω exceeding 100°. This rearprojection display is, basically, of the decenter system.

[0007] Although such an epoch-making projector can be realized, thesystem disclosed in U.S. Pat. No. 5,871,266 has some disadvantages. Thereflecting mirrors of the imaging system, as compared with refractingoptical elements, must be formed in a high surface accuracy, which willbe readily understood from the imagination of the state of reflection ofimaging light by the reflecting mirrors. For example, suppose that alight beam emitted by the image-forming device to be focused on a pointon a screen forms a spot in a region of a reflecting surface. If theregion has a form error of λ/4, where λ is, for example, 0.55 μm, a waveaberration of about λ/2 is produced. This wave aberration causes anonnegligible reduction in the resolving power of the imaging opticalsystem. Thus, the accuracy of the catoptric system is affectedsignificantly by waviness errors in the reflecting surface.

[0008] Another disadvantage of the system is the incidence angle of alight beam from the image-forming device. As stated in claims, adivergent light beam diverging at a divergence angle of 8° or below isused to realize a simple oblique-incidence imaging optical system. Inthis patented invention, all the systems including an illuminatingsystem are optimized to enhance the efficiency of light. However, thesystem has only a narrow application field because of variousrestrictions on the size of an available light source, and the size andcosts of the device.

[0009] An invention disclosed in JP-A No. Hei 10-206791 relates to aprojector of the decenter system. As shown in FIG. 29, this inventionincludes an imaging system 30 employing decentered optical elements andfree-form surfaces to increase the degree of freedom of design, andrealizes a projection system having a maximum field angle 2ω exceeding68°. The imaging system 30 is used as an imaging system for obliqueprojection as shown in FIG. 30. In FIG. 30, two conjugate planes 2 and 4are substantially parallel. Although such decentered optical elementsare employed, the field angle is not increased and, on the other hand,difficulty in fabricating and assembling parts is enhanced.

[0010] Some known optical systems of the decenter system have beendescribed by way of example. Known optical systems of the tilt systemwill be described hereinafter.

[0011]FIG. 31 illustrates an invention disclosed in U.S. Pat. No.5,274,406 relating to a projector particularly for a rear-projectiondisplay. This projector includes a symmetric projection lens 30consisting of refracting optical elements shown in FIG. 32, and afree-form surface mirror 301 having minute setbacks similar to those ofa Fresnel lens as shown in FIG. 33(b) and disposed near an image plane.The optical axis of the projection lens 30 is tilted relative to ascreen 4 and an image-forming device 2 to form the rear-projectionprojector in a small depth. A distortion resulting from the tilting ofthe optical axis is corrected by a free-form surface mirror shown inFIG. 33(a), and problems relating to the mismatch of imaging conditionsresulting from the use of such mirrors are dealt with by forming minutesetbacks similar to those of a Fresnel lens in their surfaces.

[0012] Thus, a rear-projection display provided with a 36 in. screenhaving a diagonal length 36 inch is formed in a thickness of 28 cm,which is smaller than a target thickness, because it is said that anormal number of the target thickness in inch equal to a normal numberof the diagonal of the screen in centimeter. Although therear-projection display can be thus formed in a small thickness, thedistance D₁ between the projection lens 30 and the free-form surfacemirror 301 along an optional light beam is greater than the distance D₂between the free-form surface mirror 301 and the screen along the samelight beam, and hence the free-form surface mirror 301 is necessarilylarge. Therefore, the fabrication of the free-form surface mirror havingthe setbacks similar to those of a Fresnel lens is very difficult. Thefree-form surface mirror 301 having a surface resembling that of aFresnel lens and employed to prevent the reduction of resolving powerhas the finite stepped construction and the steps reduces resolvingpower.

[0013]FIG. 34 shows other oblique-incidence imaging optical systems ofthe tilt system disclosed in JP-A Nos. Hei 06-265814 and Hei 07-151994.These oblique-incidence imaging optical systems employs a plurality ofoptical systems of the tilt system to correct a distortion. For example,an oblique-incidence imaging optical system shown in FIG. 35 has twooptical systems of the tilt system. Alight beam emitted by animage-forming device included in a plane 2 is focused by a first imagingsystem 3 to form an intermediate image on a plane 4. A second imagingsystem 3′ forms an image of the intermediate image on a screen 4′.Theoretically, it is possible to correct the distortion and to preventthe reduction of resolving power by properly determining the angle,magnification, focal length and such of each optical system so as tomeet predetermined conditions. Since the respective optical axes of theimaging systems 3 and 3′ of this oblique-incidence imaging opticalsystem intersect the plane 4 on which the intermediate image is formedat predetermined angles. Therefore the light beam must travel from theoptical system 3 to the optical system 3′ without being shaded.Generally, a pupil-coupling device, such as a decentered Fresnel lens asshown in FIG. 36, is disposed at a position where the intermediate imageis formed to enable the light beam to travel from the optical system 3to the optical system 3′ without being shaded. For example, if theimage-forming device has minimum pixel construction like a liquidcrystal panel, a moiré pattern is formed by interference with theperiodic construction of the Fresnel lens. This problem is solved bydisplacing the pupil-coupling device from a position corresponding tothe intermediate image.

[0014] This oblique-incidence imaging optical system is disadvantageousin that the respective optical axes of the optical systems 3 and 3′ areinclined at a large angle to the intermediate image 4 or theimage-forming device 2 and it is often difficult to meet mechanicalrequirements. Detailed description of the problem will be omittedherein. The pupil-coupling device shown in FIG. 36 is one of problemsdifficult to solve.

[0015]FIG. 37 shows an imaging optical system disclosed in JP-A No. Hei07-13157. A collimated light beam emitted by a light source la falls onan image-forming device 2. A first paraboloidal reflector 3 aconcentrates the light beam reflected by the image-forming device 2 onthe pupil of a projection lens 3 b. The light beam traveled through theprojection lens 3 b is reflected by a second paraboloidal reflector 3 cto form an enlarged image on a screen 4. Basically, this imaging opticalsystem is of the tilt system. The first paraboloidal reflector 3 a isused for coupling the projection lens 3 b and an illuminating lightbeam, and the second paraboloidal reflector 3 c is used to make thelight beam fall on the screen 4 in a direction at a fixed angle to thescreen 4 to form a thin rear projection display. Although it is unknownwhether the invention is practically realizable because concreteexamples are not mentioned in the specification, it is considered thatthis imaging optical system is unable to meet practical opticalrequirements.

[0016]FIG. 38 shows an imaging optical system of the tilt systemdisclosed in JP-A No. Hei 09-179064. This imaging optical system,similarly to those disclosed in U.S. Pat. No. 5,871,266 and JP-A No. Hei07-13157, includes, in combination, an imaging system 30 consisting ofrefracting optical elements, and a concave reflector 31. A light beamemitted by an image-forming device 2 travels through the optical system30 consisting of refracting optical elements 3 a to 3 g shown in FIG.39, is reflected by the concave reflector 31 and falls obliquely on ascreen 4. This imaging optical system utilizes the characteristics of anafocal system for correcting a distortion produced by the tilt system.

[0017] When an afocal system is constituted of two optical elements 30and 31 such that the distance between the optical elements 30 and 31 isequal to the sum of the respective focal lengths of the optical elements30 and 31 as shown in FIG. 40, the magnification of the afocal systemremains constant regardless of an object distance. A distortion can becorrected by constituting such an optical system of a refracting opticalelement 30 having a positive focal length and a concave reflector 31having a positive focal length, and by making a light beam fall on ascreen 4 at a fixed angle to the screen 4.

[0018] In an embodiment of this known optical system, a light beam fallson the screen 4 in an object plane at a large angle of, for example, 70°to a normal to the screen 4. A decentered optical element and afree-form surface are employed to secure a degree of freedom to reducethe distortion further and to improve resolving power. This system isdisadvantageous in that the afocal system is constituted of the twooptical elements, and the distance between the optical elements 30 and31 must be unavoidably increased to form an enlarging system; that is,when the distance between the projection lens 30 and the concavereflector 31 along a light beam is D1 and the distance between theconcave reflector 31 and the screen 4 along a light beam is D2, D1>D2for most part of the light beam and hence the concave reflector 31 mustbe necessarily large, which causes problems in the mass production ofthe concave reflector 31.

[0019] The foregoing examples are techniques mainly relating toprojectors. Let us examine some examples of head-mounted displays (HMDs)as other possible use of oblique-incidence imaging optical systems.

[0020] Important matters to be taken into account in designing ahead-mounted display are: wideness of angle of field (large enlargedimage), smallness of dimensions, and lightness.

[0021] Regarding angle of field, a necessary size of an image-formingdevice is substantially dependent on the connection with an angleincluding an image-forming device when a necessary angle of field isspecified, because the size of a pupil is substantially fixed. FIG. 41shows a standard HMD. A relay optical system 30 focuses a light beamfrom an image-forming device 2 to form an intermediate image 4, and aconcave mirror 31 enlarges the intermediate image to provide an enlargedimage. The enlarged image is observed with an eye at a position 303. Theconcave mirror 31 concentrates principal light beams on the pupil.Basically, this HMD is a coaxial system, which is an optical system easyto design. However, since the eye must be spaced from the concave mirror31, and the relay optical system 30 needs a space for installation, theHMD is inevitably considerably large.

[0022]FIG. 42 shows the optical system of a HMD disclosed in JP-A No.Hei 05-303055. An imaging optical system including a relay opticalsystem 30 focuses a light beam from an image-forming device 2 to form animage, and a concave mirror 31 enlarges the image to provide an enlargedimage. The enlarged image is observed with an eye at a position 301.Basically, this HMD is the same in configuration as the aforesaid HMD.This HMD omits a beam splitter and employs a decentered system to formthe HMD in s small thickness. Thus, this HMD is an oblique-incidenceimaging optical system of the tilt system.

[0023] A HMD disclosed in JP-A NO. 07-191274 is obtained by introducingimprovements in the HMD disclosed in JP-A No. Hei 05-303055. As shown inFIGS. 43 and 44, one concave mirror is replaced with a plurality ofconvex mirrors and concave mirrors to improve the correction ofaberration. Addition of the convex mirror increases the degree offreedom of high aberration correction and widens the width of design.The reflector closest to the eye is a concave mirror. A HMD in anembodiment has a relay optical system 30 consisting of reflectors andconsisted entirely of a catoptric system. This HMD is analogous with theprojection optical system of the projector disclosed in U.S. Pat. No.5,871,266 in constituting the optical system only of reflectors.

[0024]FIG. 45 shows a HMD disclosed in JP-A No. Hei 10-239631. This HMDis formed in compact construction by folding the arrangement of thereflectors of the HMD disclosed in JP-A No. Hei 07-191274 in a space.Although the HMD is small, aberration is corrected effectively by meansof two refracting surfaces 301 and 304 and two reflecting surfaces 302and 303. To secure degree of freedom, optical surfaces are free-formsurfaces. This system is epoch-making for applications in which twoimage-forming device s for both eyes can be used and a comparativelylarge f number is permitted.

[0025] Although examples of optical systems in the two fields ofapplication of the oblique-incidence imaging optical system have beendescribed, the oblique-incidence imaging optical system is applicable tovarious uses, and the field of practical application of the same tovarious products has been progressively widening. For example, therehave been proposed new oblique-incidence imaging optical systems meetingcurrent requirements, such as the oblique-incidence imaging opticalsystem proposed in JP-A No. Hei 10-239631, for the field of HMDS.However, those oblique-incidence imaging optical systems areunsatisfactory in meeting future requirements for wide angle of fieldand picture quality. The degree of freedom may be increased byincreasing reflecting surfaces as mentioned above in connection withJP-A No. Hei 07-191274. However, increase in the number of reflectingsurfaces requires forming the reflecting surfaces in high accuracies andincreases the cost. Thus further technical research and development inthis field is desired.

[0026] When the oblique-incidence imaging optical system is applied to aprojector or an image pickup system, further improvement of the abilityof the oblique-incidence imaging optical system is required, because aprojector or an image pickup system requires abilities severer thatthose required of systems for visual observation. Image-forming devices,such as liquid crystal displays, and image pickup devices, such as CCDs,have been progressively miniaturized and pixels have been reduced tosizes on the order of micrometers. Consequently, optical systems havinghigh resolving power and capable of preventing reduction in lightintensity are needed. On the other hand, the miniaturization of devicesis advantageous conditions for the miniaturization of optical systems.If an image can be projected at a half field angle exceeding 70° asmentioned in U.S. Pat. No. 5,871,266, a display can be formed in athickness equal to ⅓ of the thickness of the conventional display, andcan be applied to various input/output devices including a videophonesystem disclosed in JP-A No. Hei 06-133311 as shown in FIG. 46,projectors, thin image readers capable of reading an image at a stroke,such as image scanner, stereoscopic image readers and cameras.

[0027] Thus, a technical subject of the present invention is to increasemeans for realizing an oblique-incidence imaging optical system as muchas possible. Unfortunately, the conventional optical systems have someproblems in brightness, resolving power, size, productivity and/orcosts, and only few conventional oblique-incidence imaging opticalsystems are widely applicable to many uses.

[0028] It is an object of the present invention provides new means forrealizing an oblique-incidence image-forming optical system and to applythe same to various uses.

[0029] Another object of the present invention is to provide means forrealizing a bright oblique-incidence image-forming optical systemcapable of projecting an image at a half field angle exceeding 70° whichcould not be achieved by prior art and of controlling distortion.

DISCLOSURE OF THE INVENTION

[0030] According to the present invention, it is a first condition thata light beam on a point in a predetermined range contributing to imageformation on a first conjugate plane A of conjugate planes in an imagingoptical system diverges at a divergence angle of 10° or greater. It is asecond condition that an optical system includes, as essentialcomponents, a first optical system consisting of a plurality of opticalelements and capable of converging a light beam at least around itsreference axis, and a second optical system capable of making a lightbeam diverge at least around its reference axis. A light beam emittedfrom the first conjugate plane A travels through the first and thesecond optical system and is converged on a second conjugate plane B.

[0031] The optical systems are formed so as to meet predeterminedconditions in relation with the optical beam traveling through theoptical systems. Suppose that the distance between the first opticalsystem and the second optical system along the reference axis of thefirst optical system is S1, and the distance between the second opticalsystem and the second conjugate plane B along the reference axis of thesecond optical system is S2. Suppose, in relation with an optional lightbeam emerging from the first optical system, that distance to a firstconverging point where the distance along the reference axis of thefirst optical system in a section of the light beam including principalrays is the longest is L1, and distance to a second converging pointwhere the distance along the reference axis of the first optical systemin a section of the light beam different from the aforesaid section isthe shortest is L2. The distance L1 relating to a light beam emergingfrom a position the nearest to the reference axis of the first opticalsystem among the thus calculated distances L1 is L11, the distance L2relating to a light beam emerging from a position the nearest to thereference axis of the first optical system among the thus calculateddistances L2 is L21, the distance L1 relating to a light beam emergingfrom a position the remotest from the reference axis of the firstoptical system among the thus calculated distances L1 is L1 n, and thedistance L2 relating to a light beam emerging from a position theremotest from the reference axis of the first optical system among thethus calculated distances L2 is L2 n. Then, the following conditionsmust be satisfied.

S 1≦L 11≦S 1+S 2

S 1≦L 21≦S 1+S 2

L 11/L 1 n<0.25

|L 2/L 2 n<1.5

[0032] In relation with any light beam emerging from a predeterminedrange on the first conjugate plane A and concentrated on the secondconjugate plane B, suppose that the distance between the first and thesecond optical system along the light beam is D1, and the distancebetween the second optical system and the second conjugate plane B alongthe beam is D2. Then, the following condition must be satisfied.

D1<D2

[0033] Preferably, the imaging optical system meets at least one ofconditions expressed by:

S 1/L 11>0.6

(S 1+S 2)/L 2 n<1

ΔSL>0.6

[0034] where S1 is the distance between the first and the second opticalsystem along the reference axis of the first optical axis, S2 is thedistance between the second optical system and the second conjugateplane B along the reference axis of the second optical system, L11 isthe distance relating to a light beam emerging from a part the nearestto the reference axis of the first optical system among the distances L1to the first converging points in a section of the optical beam, L2 n isthe distance relating to a light beam emerging from a position theremotest from the reference axis of the first optical system among thedistances L2 to the second converging point, and ΔSL is the differencebetween a maximum S1/L1 and a minimum S1/L1 relating to each light beam.

[0035] The imaging optical system is capable of either an imagingfunction to form an enlarged image of the conjugate plane A on theconjugate plane B or an imaging function to form a reduced image of theconjugate plane B on the conjugate plane A.

[0036] Desirably, in the imaging optical system, each of the first andthe second optical system includes an optical element having at leastone aspherical surface or a free-form surface.

[0037] In the imaging optical system, the first optical system mayprincipally comprise refracting optical elements, and the second opticalsystem may principally comprise reflecting optical elements.

[0038] In the imaging optical system, the first and the second opticalsystems may principally comprise reflecting optical elements

[0039] In the imaging optical system, at least either the first or thesecond optical system may include an optical element decentered from itsreference axis.

[0040] In the imaging optical system, at least either the first or thesecond optical system may include a rotationally symmetric opticalelement.

[0041] In the imaging optical system, each of the first and the secondoptical system may include rotationally symmetric optical elementshaving a common axis of rotation symmetry, and the reference axes of thefirst and the second optical system may be aligned with the axis ofrotation symmetry.

[0042] In the imaging optical system, all the light beams are inclinedat angles not smaller than 45° to a normal to the conjugate plane B.

[0043] In the imaging optical system, the divergence of the light beamat a cone angle of 10° or greater is important for the oblique-incidenceimaging optical system to maintain a fixed brightness. Thus, the imagingoptical system is bright, and the field of application of theoblique-incidence imaging optical system of the present invention can beexpanded.

[0044] When the condition expressed by: D2>D1, where D1 is the distancebetween the first and the second optical system along an optional lightbeam and d2 is the distance between the second optical system and theconjugate plane B along the same light beam, is satisfied, excessiveincrease in the sizes of the optical elements of the second opticalsystem can be prevented, whereby practical problems in the opticalsystem relating to the size of the imaging optical system, and themass-productivity and costs of the elements can be solved.

[0045] The converging function of the part around the reference axis ofthe first optical system, and the diverging function of the part aroundthe reference axis of the second optical system, in combination withsome other conditions, are effective in avoiding the enlargement of theimaging optical system and are conditions for realizing anoblique-incidence imaging optical system of comparatively simpleconstruction having a large field angle. This imaging optical system isadvantageous when applied to a projector or the like that needs a longback focal length.

[0046] When the distance L11 relating to a light beam emerging from aposition the nearest to the reference axis of the first optical axisamong the distances L1 to a convergence point at the longest distancealong the reference axis of the first optical system in sectionsincluding principal rays of an optional light beam emerging from thefirst optical system, and the distance L21 relating to the light beamemerging from the position the nearest to the reference axis of thefirst optical system among the distances L2 to a convergence point atthe shortest distance along the reference axis of the first system meetthe following conditions:

S 1≦L 11≦S 1+S 2

S 1≦L 21≦S 1+S 2

[0047] the diverging function of the second optical system on the sideof the reference axis is balanced and, in combination with conditionsrelating light beams apart from the reference axis, an oblique-incidenceimaging optical system is realizable. The aforesaid two conditionsrelate to the light beam the nearest to the reference axis of the firstoptical system and signifies that converging points in all the sectionsof the light beam lie between the second optical system and theconjugate plane b.

[0048] The distance L1 n relating to a light beam emerging from aposition the remotest from the reference axis of the first opticalsystem among the distances L1 to the converging point at the greatestdistance along the reference axis of the first optical system meets thefollowing condition.

L 11/L 1 n<0.25

[0049] This condition must be met to match the condition of the opticalsystem for aberration correction at a position distant from thereference axis of the second optical system, and this is done by makingthe distance L1 to the converging point of the light beam differentbetween the light beam near the reference axis of the first opticalsystem and the light beam far the reference axis of the first opticalsystem. Although the distances L1 and L2 are measured along thereference axis of the first optical system, when the convergent lightbeam in the section of the light beam becomes divergent and an imaginaryconverging point lies on the opposite side of the first optical system(the distance is negative), the distances L1 and L2 are handled as aconverging point (distance) further than infinity. Thus, a conditionalexpression can be obtained without contradiction.

[0050] The imaging optical system of the present invention mustbasically meet a condition:

|L 21/L 2 n|<1.5

[0051] where L21 is the distance relating to a light beam emerging froma position the nearest to the reference axis of the first optical systemamong the distances L2, and L2 n is the distance L2 relating to a lightbeam emerging from a position the remotest from the reference axis ofthe first optical system among the distances L2.

[0052] The background of the basic idea relating the foregoingconditions will be explained prior to the description of otherconditions.

[0053] An optical system for a practical oblique-incidence imagingoptical system must be small and simple in construction. When combiningthe diverging first optical system and the converging second opticalsystem in the vicinity of the reference axis as the basic constructionaccording to the present invention, it is important to miniaturize andsimplify the diverging second optical system. Although the respectivefunctions of the first and the second optical system cannot becompletely separated, the principal function of the second opticalsystem is to distribute the light beams at desired positions on theconjugate plane B. When simplifying the second optical system, most ofthe degree of freedom of the second optical system is used for thispurpose. Accordingly, the principal function of the first optical systemis to match the imaging condition for the light beam that cannot bematched by the second optical system, and angular condition and tomaintain the balance of the entire optical system. As mentioned above,the conditions conflicting with each other can be satisfied and adesired oblique-incidence imaging optical system can be realized bysimultaneously satisfying the four conditions relating to the convergingposition of the light beam in addition to the basic constructionalconditions.

[0054] The three following conditions are favorable for forming animaging optical system which projects an image obliquely on a screen ata very large angle of incidence.

S 1/L 11>0.6

(S 1+S 2)/L 2 n<1

ΔSL>0.6

[0055] These conditions are important for realizing a projector thatprojects an image on a screen from a position very close to the screen,and a very thin rear projection display. Desirably, these projectorsmeet at least one of the three conditions.

[0056] The imaging optical system of the present invention can be usedas an enlarging optical system which uses the conjugate plane A as anobject plane and forms an enlarged image of the conjugate plane A on theconjugate plane B. An optical system of the same configuration can beused as a reducing optical system which forms a reduced image of theconjugate plane B on the conjugate plane A.

[0057] The employment of an optical element having at least oneaspherical or free-form surface in the optical system increases thedegrees of freedom of design, is an essential condition for realizingthe function of each optical system, and satisfies requiredspecifications by the simplest possible construction. It is moreeffective that both the first and the second optical system are providedwith such optical elements.

[0058] It is important to avoiding problems relating to the fabricationof the reflecting systems and to providing a realizableoblique-incidence imaging optical system that the first optical systemcomprises mainly a plurality of refracting optical elements, and thesecond optical system comprises mainly reflecting optical elements. Theoptical system can be simplified and the cost of the same can be reducewhen the second optical system comprises a single reflecting opticalelement.

[0059] Although the formation of both the first and the second opticalsystem mainly of reflecting optical elements makes the mass productionof the oblique-incidence imaging optical system difficult, the use ofreflecting optical elements as principal components enables therealization of a very thin oblique-incidence imaging optical systemcapable of displaying a brighter image by applying the basic conditionsof the present invention. The use of reflecting optical elements incombination with techniques for fabricating reflecting optical elementsis a prospective future technique.

[0060] The degree of freedom of design of the entire optical system canbe increased by providing at least one of the conjugate plane A, thefirst optical system, the second optical system and the conjugate planeB of the optical system and the component optical elements of thosecomponents with a degree of freedom of decentering.

[0061] If at least either the first optical system or the second opticalsystem can be constituted of rotationally symmetric optical elements,the conventional manufacturing method and assembling method can be usedand hence the manufacturing costs can be reduced and ease of assemblingthe optical system can be greatly improved. If all the rotationallysymmetric optical elements have a common axis of rotation symmetry, andthe common axis of rotation symmetry coincides with the reference axesof the optical systems, further effects can be expected.

[0062] Problems in applying the optical system to practical uses in aspecific field can be solved by projecting all the light beams on theconjugate plane B at an angle not smaller than a predetermined angle toa normal to the conjugate plane B. For example, problems in the screenof a reverse projector and problems in a space in which a projector isto be installed can be solved.

BRIEF DESCRIPTION OF THE DRAWINGS

[0063]FIG. 1 is a sectional view of a projector, i.e., anoblique-incidence imaging optical system, in a first embodimentaccording to the present invention;

[0064]FIG. 2 is a diagrammatic view showing the convergence of lightbeams emerging from a first optical system included in the projector inthe first embodiment;

[0065]FIG. 3 is a sectional view of the first optical system of theprojector in the first embodiment;

[0066]FIG. 4 is a sectional view of a projector, i.e., anoblique-incidence imaging optical system, in a second embodimentaccording to the present invention;

[0067]FIG. 5 is a diagrammatic view showing the convergence of lightbeams emerging from a first optical system included in the projector inthe second embodiment;

[0068]FIG. 6 is a sectional view of a projector, i.e., anoblique-incidence imaging optical system, in a third embodimentaccording to the present invention;

[0069]FIG. 7 is a diagrammatic view showing the convergence of lightbeams emerging from a first optical system included in the projector inthe third embodiment;

[0070]FIG. 8 is a sectional view of the first optical system included inthe projector in the third embodiment;

[0071]FIG. 9 is a sectional view of a projector, i.e., anoblique-incidence imaging optical system, in a fourth embodimentaccording to the present invention;

[0072]FIG. 10 is a front elevation of the projector in the fourthembodiment;

[0073]FIG. 11 is a diagrammatic view showing the convergence of lightbeams emerging from a first optical system included in the projector inthe fourth embodiment;

[0074]FIG. 12 is a sectional view of the first optical system includedin the projector in the fourth embodiment;

[0075]FIG. 13 is a sectional view of a rear projection display, i.e., anoblique-incidence imaging optical system, in a fifth embodimentaccording to the present invention;

[0076]FIG. 14 is a front elevation of the rear projection display in thefifth embodiment;

[0077]FIG. 15 is a diagrammatic view showing the convergence of lightbeams emerging from a first optical system included in the rearprojection display in the fifth embodiment;

[0078]FIG. 16 is a sectional view of the first optical system and asecond optical system included in the rear projection display in thefifth embodiment;

[0079]FIG. 17 is a sectional view of a rear projection display, i.e., anoblique-incidence imaging optical system, in a sixth embodimentaccording to the present invention;

[0080]FIG. 18 is a front elevation of the rear projection display in thesixth embodiment;

[0081]FIG. 19 is a sectional view of a first optical system included inthe rear projection display in the sixth embodiment;

[0082]FIG. 20 is a sectional view of a projector in a seventh embodimentaccording to the present invention;

[0083]FIG. 21 is a sectional view of a first optical system included inthe projector in the seventh embodiment;

[0084]FIG. 22 is a sectional view of a rear projection display in aneighth embodiment according to the present invention;

[0085]FIG. 23 is a sectional view of a rear projection display in aninth embodiment according to the present invention;

[0086]FIG. 24 is a diagrammatic view of assistance in explaining theprinciple of an oblique-incidence imaging optical system of the decentersystem;

[0087]FIG. 25 is a diagrammatic view of assistance in explaining theprinciple of an oblique-incidence imaging optical system of the tiltsystem;

[0088]FIG. 26 is a conceptual diagrammatic view of assistance inexplaining the distortion of an image formed by an oblique-incidenceimaging optical system of the tilt system;

[0089]FIG. 27 is a sectional view of a projection lens disclosed in JP-ANo. Hei 05-273460;

[0090]FIG. 28 is a sectional view of a projector disclosed in U.S. Pat.No. 5,871,266;

[0091]FIG. 29 is a sectional view of a projection lens disclosed in JP-ANo. Hei 10-206791;

[0092]FIG. 30 is a sectional view of assistance in explaining a mode ofimage projection by the projector disclosed in JP-A No. Hei 10-206791;

[0093]FIG. 31 is a sectional view of a rear projection display disclosedin U.S. Pat. No. 5,274,406;

[0094]FIG. 32 is a sectional view of a projection lens included in therear projection display disclosed in U.S. Pat. No. 5,274,406;

[0095]FIG. 33 is a perspective view of Fresnel mirrors employed in therear projection display disclosed in U.S. Pat. No. 5,274,406;

[0096]FIG. 34 is a sectional view of a projection optical systemincluded in an oblique-incidence imaging optical system disclosed inJP-A No. Hei 06-265814;

[0097]FIG. 35 is a diagrammatic view of assistance in explaining amultistage tilt system;

[0098]FIG. 36 is a sectional view of a pupil-coupling element employedin the multistage tilt system;

[0099]FIG. 37 is a sectional view of a rear projection display disclosedin JP-A No. Hei 07-13157;

[0100]FIG. 38 is a sectional view of a projector disclosed in JP-A No.Hei 09-179064;

[0101]FIG. 39 is a sectional view of a projection lens included in theprojector disclosed in JP-A No. Hei 09-179064;

[0102]FIG. 40 is a diagrammatic view of assistance in explaining theprinciple of an afocal tilt system;

[0103]FIG. 41 is a sectional view of a typical head-mounted display(HMD);

[0104]FIG. 42 is a sectional view of a HMD disclosed in JP-A No. Hei05-303055;

[0105]FIG. 43 is a sectional view of a HMD disclosed in JP-A No. Hei07-191274;

[0106]FIG. 44 is a sectional view of a HMD disclosed in JP-A No. Hei07-191274;

[0107]FIG. 45 is a sectional view of a HMD disclosed in JP-A No. Hei10-239631; and

[0108]FIG. 46 is a conceptual view of a videophone system disclosed inJP-A No. Hei 06-133311.

BEST MODE FOR CARRYING OUT THE INVENTION

[0109] Preferred embodiments of the present invention will be describedwith reference to the accompanying drawings.

[0110] The present invention can be embodied in various things in manydifferent fields and it needless to describe all the embodiment of thepresent invention. The invention will be described in terms of aprojector for forming an enlarged image of an image-forming device 2included in a conjugate plane A on a screen 4 included in a conjugateplane B. Although the projector needs an illuminating system, only animaging optical system and the associated systems will be describedbecause the illuminating system is not essential to the presentinvention. The accompanying drawings show only parts, devices andsystems necessary for the description of the present invention andothers unnecessary for the description are omitted.

[0111] Each of a first to a seventh embodiment has a first and a secondoptical system each comprising optical elements having a common axis ofrotation symmetry. In those embodiments, the respective reference axesof the first and the second optical system are aligned with a commonaxis, i.e., an optical axis. Similarly, the image-forming device 2 andthe screen 4 are perpendicular to the optical axis and are parallel toeach other. Each of an eighth and a ninth embodiment employs adecentered system and a free-form surface, i.e., a rotationallyasymmetric system. Effect of increase in the degree of freedom of designwill be confirmed through the examination of the eighth and the ninthembodiment.

[0112]FIG. 1 is a sectional view of a projector in a first embodimentaccording to the present invention.

[0113] An imaqe-forming device 2 is included in a conjugate plane A. Theimage-forming device 2 is a transmission liquid crystal display having adiagonal length of 0.7 in. and an aspect ratio of 4:3. An illuminatingunit, not shown, for illuminating the image-forming device 2 is disposedon the left side of the image-forming device 2. Light beams emergingfrom the image-forming device 2 travel through a first optical system 30comprising refracting optical elements, are reflected by a reflectingmirror included in a second optical system 31 to form an enlarged imageof 100 in. on a screen 4 included in a conjugate plane B.

[0114] The first optical system 30 and the second optical system 31 havereference axes 3A and 3B, respectively. The first optical system 30converges parallel light beams coming from an object point at infinityin the vicinity of its reference axis 3A, and the second optical system31 diverges the light beams in the vicinity of its reference axis 3B.The image-forming device 2 is disposed below the reference axis 3A ofthe first optical system 30, as viewed in FIG. 1. A light beam 321traveled through a point the nearest to the reference axis 3A of thefirst optical system 30 falls on a lower part of the screen 4. A lightbeam 328 traveled through a point the remotest from the reference axis3A falls on an upper part of the screen 4. The distance S2 between thesecond optical system 31 and the screen 4 along the reference axis 3B is2 m. An imaging optical system including the optical systems 30 and 31is disposed on a level below the screen 4 and projects an imageobliquely upward onto the screen 4. Thus, the imaging optical system isa front projection display that projects an image on the screen from thefront side of the screen.

[0115]FIG. 2 shows the light beams 311 to 318 traveled through the firstoptical system 30 and not acted upon by the second optical system 31.The light beams shown in FIG. 2 are supposed to have penetrated thesecond optical system 31 without being reflected by the reflectingmirror of the second optical system 31. The distance between the screen4 and the second optical system 31 along the reference axis 3B is 2 m.The light beams farther from the reference axis 3B in FIG. 2 are thosefarther from the reference axis 3A. In FIG. 2, points marked with ablank triangle (Δ) are converging points of the light beams in the paperwhere the diameters of the sections of the light beams are smallest, andpoints marked with a solid circle () are converging points in a sectionperpendicular to the paper. A curve 31T connects the converging pointsmarked with a blank triangle, and a curve 31S connects the convergingpoints marked with a solid circle. Each converging point marked with asolid circle is the distance to the nearest converging point along thereference axis 3A of the first optical system 30 among all the sectionsof the light beam. Similarly, each converging point marked with a blanktriangle corresponds to the longest converging point.

[0116] It is understood from FIG. 2 that the converging point markedwith a blank triangle of a light beam in the paper traveled through thefirst optical system 30 is farther from the first optical system 30, andthe angle of convergence at the converging point decreases graduallywhen the light beam emerges from a part of the first optical systemfather from the reference axis 3A. The distance of the converging pointmarked with a solid circle in a section perpendicular to it does notchange greatly. In this description, the term, “converging angle”signifies a maximum cone angle at the converging point in the section ofthe light beam. With a divergent pencil of rays diverging after thefirst optical system 30, converging angle is a negative maximum coneangle. Even in the case that a light beam converges gradually and afterthat the light beam starts diverging, it can be said that convergingangle unitarily decreases.

[0117] In a practical optical system, the screen 4 extends into thepaper and light beams travel and fall on the two-dimensional surface ofthe screen 4. If all the light beams are shown in FIG. 2, the drawingwill be very complicated and hence all the light beams are not shownintentionally. Regarding those, numerical data is tabulated togetherwith other embodiments in Table 3 showing conditions for realizing thepresent invention. In the case of this example, all the convergingpoints relating to optional light beams having principal rays in thepaper are formed between the second optical system 31 and the screen 4included in the conjugate plane B. As shown in table 3, light beams notextending in the paper, traveling toward the diagonal of the screen 4,and separated from the reference axis have converging points atpositions beyond the screen 4.

[0118]FIG. 3 is a sectional view of the first optical system 30. Thefirst optical system 30 comprises six groups of eight refracting opticalelements. All the surfaces have rotationally symmetric shapes havingaxis of symmetry coinciding with the reference axis 3A. In a generaloptical system including a decentered system, such correspondence doesnot hold good. In such a case, an optional reference axis may beselected; a most rational or convenient axis may be used as a referenceaxis. Light beams emerging from the image-forming device 2 travelsequentially across refracting surfaces r1, r2, . . . , and r14 in thatorder to the second optical system 31. The distance of travel of thelight beams from the first optical system 310 along the reference axisof the first optical system 30 is measured along the reference axis 3Afrom the apex of the surface r14. Since the first optical system 30 is arotationally symmetric system, focal length in an ordinary sense can bedefined. In this case, the focal length f=37.1 mm.

[0119] Table 1 shows the exit angles of the principal rays of the lightbeams 311 to 318 after passing through the first optical system 30. InTable 1, the term, “image height” signifies the distance between thereference axis 3A of the first optical system 30 and an exit point fromwhich the corresponding light beam emerges from the image-forming device2, the term, “actual exit angle” signifies an actual angle between theprincipal ray of the light beam and the reference axis 3A, and the term,“calculated exit angle” signifies a calculated exit angle θ calculatedby using: h=f×tan θ, where h is image height and f is focal length. Itis known from Table 1 that the difference between the actual exit angleand the calculated exit angle of the light beam farther from thereference axis 3A is greater than that of the light beam nearer to thereference axis 3A. The calculated exit angle and the actual exit angleof the light beam near the reference axis 3A are scarcely different.TABLE 1 Light beam Actual exit Calculated number Image height angle exitangle 311 3.50 5.41 5.39 312 5.00 7.74 7.67 313 6.50 10.09 9.93 314 8.0012.45 12.16 315 9.50 14.83 14.36 316 11.00 17.25 16.51 317 12.50 19.7018.61 318 14.17 22.48 20.89

[0120] The reflecting mirror 31 included in the second optical system 31shown in FIG. 1 is a rotationally symmetric aspheric mirror having anaxis of rotation coinciding with the reference axis 3B. Thus, theoptical axis coincides with the reference axis 3B. A part of thereflecting mirror around the reference axis 3B is a convex surfacehaving a radius of curvature of about 400 mm and capable of divergingthe incident light beams. The focal length f of the same part of thereflecting mirror is −200 mm.

[0121] In this embodiment, the optical systems 30 and 31 are disposedsuch that the respective reference axes thereof are aligned and hencethe optical systems 30 and 31 have a common optical axis. The focallength f of a part around the optical axis of a composite systemincluding the optical systems 30 and 31 is 14.7 mm. Table 2 showscalculated exit angles of the light beams after being reflected by thesecond optical system 31 calculated on the basis of angles between thelight beams and the optical axis and the focal length of the compositesystem. Although slightly different, the actual and calculated exitangles agree closely with each other.

[0122] A TV distortion caused by this embodiment is 0.5% or below. TABLE2 Light beam Actual exit Calculated number Image height angle exit angle311 3.50 13.38 13.39 312 5.00 18.75 18.78 313 6.50 23.77 23.84 314 8.0028.39 28.54 315 9.50 32.58 32.86 316 11.00 36.36 36.79 317 12.50 39.7940.36 318 14.17 43.24 43.93

[0123] The distance S1 along the common optical axis between the firstoptical system 30 and the second optical system 31 is 280 mm, and thedistance S2 between the second optical system 31 and the screen 4 is2000 mm. Thus, it is obvious that the distance D1 along an optionallight beam between the first optical system 30 and the second opticalsystem 31, and he distance D2 along the same light beam between thesecond optical system 31 and the screen 4 meets an inequality: D2>D1.The first optical system 30 receives a light beam having a cone angle of23° (f number of 2.5) from an optional point on the image-forming device2 and secures sufficient brightness for a projecting system. Theimage-forming device 2 and the screen 4 are parallel to each other andthe common optical axis aligned with the reference axes 3A and 3B is anormal to both the image-forming device 2 and the screen 4.

[0124] Necessary conditions for the imaging optical system according tothe present invention will be examined hereinafter. TABLE 3 ImageEmbodiment S1 S2 height L1 φ2 L2 φ1 Embodiment 1 280 2000 1 490.2 0.0475.1 90.0 n 2594.1 27.0 723.0 117.0 Embodiment 2 300 700 1 517.3 0.0479.8 90.0 n 7433.2 24.0 440.8 114.0 Embodiment 3 300 450 1 432.2 0.0409.4 90.0 n −1750.3 27.0 790.0 117.0 Embodiment 4 300 700 1 412.9 0.0403.8 90.0 n −734.1 12.0 987.5 102.0 Embodiment 5 230 520 1 404.9 0.0359.0 90.0 n −495.0 24.0 736.1 114.0 Embodiment 6 280 750 1 421.9 0.0392.3 90.0 n −373.7 26.0 940.3 117.0 Embodiment 7 300 167 1 454.1 0.0368.4 90.0 n −430.9 0.0 716.7 90.0 Embodiment 8 97 257 1 154.9 0.0 141.390.0 n −112.6 26.0 409.4 115.5 Embodiment 9 80 205 1 109.8 0.0 106.590.0 n −132.0 40.0 342.9 117.0

[0125] Table 3 shows converging positions where light beams converge inembodiments including those which will be described later. Shown inTable 3 are distance S1 along the reference axis of the first opticalsystem between the first an the second optical system, distance S2 alongthe reference axis of the second optical system between the secondoptical axis and the conjugate plane B, distance L1 to a convergingpoint in a section of a light beam that makes distance along thereference axis of the first optical system longest, and distance L2 to aconverging point in another section of a light beam that makes distancealong the reference axis of the first optical system shortest only thevalues of L1 and L2 for L11 and L12 (lines in which the image heightis 1) emerging from a part the nearest to the reference axis of thefirst optical system and L1 n and L2 n (lines in which the image heightis n) relating to a light beam emerging from a point the remotest fromthe reference axis of the first optical system are shown. Shown inaddition to data necessary for calculation using conditional expressionsis light beam section angle immediately after emergency from theconjugate plane A as reference for light beam section angles at theconverging points L1 and L2. The shape of the wavefront of the lightbeam changes as the light beam is subjected repeatedly to reflection andrefraction and hence the light beam section angle is only a tentativestandard. TABLE 4 (S1 + S2)/ (S1 + S2)/ (S1 + S2)/ L11/ L21/ EmbodimentS1/L11 S1/L1n ΔSL L11 S1/L21 L21 L2n L1n L2n 1 0.57 0.11 0.46 4.65 0.594.80 3.15 0.19 0.66 2 0.58 0.04 0.54 1.93 0.63 2.08 2.27 0.07 1.09 30.69 −0.17 0.87 1.74 0.73 1.83 0.95 −0.25 0.52 4 0.73 −0.41 1.14 2.420.74 2.48 1.01 −0.56 0.41 5 0.57 −0.46 1.03 1.85 0.64 2.09 1.02 −0.820.49 6 0.66 −0.75 1.41 2.44 0.71 2.63 1.10 −1.13 0.42 7 0.66 −0.70 1.361.03 0.81 1.27 0.65 −1.05 0.51 8 0.63 −0.80 1.49 2.29 0.69 2.51 0.87−1.38 0.35 9 0.73 −0.61 1.34 2.60 0.75 2.68 0.83 −0.83 0.31

[0126] Table 4 shows values calculated on the basis of data shown inTable 3 to confirm conditional expressions for the embodiments. Forexample, a conditional expression: S1≦L11≦S1+S2 can be confirmed from afact shown in Table 4 that S1/L11<1 and (S1+S2)/L11>1. The same holdstrue for other conditional expressions. The basic explanation of thefirst embodiment will be now ended. A desired oblique-incidence imagingoptical system of comparatively simple construction can be realized bydetermining the basic construction of the first and the second opticalsystem and controlling the converging positions of the light beam. Thebasic idea is the use of the first optical system as a matching systemfor light beam relating to the second optical system.

[0127]FIG. 4 shows a projector in a second embodiment according to thepresent invention. An image-forming device 2 included in a conjugateplane A is a 1.3 in. transmission display. A 50 in. enlarged image isformed on a screen 4 included in a conjugate plane B. Only principalmatters different from those of the first embodiment will be described.A first optical system 30 having a reference axis 3A includes tworefracting optical elements. The refracting optical element having apositive power is disposed on the side of the image-forming device 2,and the refracting optical element having a negative power is disposedon the side of a second optical system 31. The second optical system 31having a reference axis 3B includes a single refracting optical element31. Basically, the second embodiment is analogous with the firstembodiment, except that the second optical system 31 of the secondembodiment comprises the refracting optical element.

[0128]FIG. 5 showing a mode of the convergence of light beams,corresponding to that shown in FIG. 2 relating to the first embodiment.The respective meanings of marks are the same as those of thecorresponding marks shown in FIG. 2. Actually, there are light beamsarranged in a direction into the paper including those traveling towardthe opposite angles of the screen 4 similar to those mentioned inconnection with FIG. 2.

[0129] The positions of converging points shown in FIG. 5 are similar tothose shown in FIG. 2, except that a converging point marked with ablank triangle (Δ) where a light beam 319 the farthest from thereference axis 3A converges is located behind the screen 4. Convergingpoints marked with a blank triangle in the paper are on a curve 31T. Theconverging points of light beams farther along the optical axis 3A ofthe first optical system 30 are farther from the optical axis 3A, andconverging angle decreases gradually. Converging points marked with asolid circle () in a section perpendicular to the paper are on a curve31S and are nearer to the first optical system 30. As obvious from FIG.5 and Table 3, the converging points marked with a solid circle of lightbeams farther from the reference axis 3A are closer to the first opticalsystem. The distance S2 along the reference axis 3B between the secondoptical system 31 and the screen 4 is 700 mm, and the distance s1 alongthe reference axis 3A between the first optical system 30 and the secondoptical system 31 is 300 mm. The cone angle of the light beam receivedby the first optical system 30 from the image-forming device 2 is 10° (fnumber of about 5.6). The first optical system 30 has a focal lengthf1=61.3 mm. A composite optical system consisting of the first opticalsystem 30 and the second optical system 31 has a focal length f=15.7 mm.Exit angles of light beams emerging from the first optical system 30,and calculated exit angles calculated on the basis of the focal lengthare shown in Table 5. TABLE 5 Light beam Image Actual exit Calculatednumber height angle Exit angle 311 10.00 9.46 9.27 312 12.50 11.90 11.53313 15.00 14.38 13.76 314 17.50 16.91 15.95 315 20.00 19.49 18.08 31622.50 22.12 20.17 317 25.00 24.81 22.20 318 27.50 27.58 24.18 319 29.8130.24 25.95

[0130] As shown in Table 5, the actual exit angles are greater than thecorresponding calculated exit angles, respectively. Table 6 shows actualexit angles of light beams emerging from the second optical system andcalculated exit angles calculated on the basis of the focal length ofthe composite optical system. TABLE 6 Light beam Image Actual exitCalculated number height angle Exit angle 311 10.00 24.13 32.52 31212.50 29.17 38.55 313 15.00 33.59 43.72 314 17.50 37.42 48.13 315 20.0040.75 51.89 316 22.50 43.66 55.12 317 25.00 46.21 57.89 318 27.50 48.4760.30 319 29.81 50.33 62.25

[0131] The differences between the actual exit angles and thecorresponding calculated exit angles, differing from those in the firstembodiment, are large, which suggests the insignificance of paraxialfocal length. Despite this fact, the distortion of an image formed inthe screen 4 is 0.16% or below. It is to be noted that the exit angleswith respect to the reference axis 3A of the first optical system shownin Table 5 are greatly different from those with respect to thereference axis 3B of the second optical system shown Table 8, whichindicates that the effect of the second optical system in increasing theexit angle is significant. Although the ratio of increase in exit anglein this embodiment is comparative small as compared with those in otherembodiments, the ratio between the tangents of exit angles of the lightbeam 319, i.e., the ratio between the values of tan θ, is greater thantwo.

[0132]FIG. 6 is a sectional view of a projector in a third embodimentaccording to the present invention. An image-forming device 2 is a 0.9in. reflection display. A 60 in. enlarged image of an image formed bythe image-forming device 2 is formed on a screen 4 by a first opticalsystem 30 including refracting optical elements, and a second opticalsystem 31 including a single reflecting mirror. The optical axis of theprojector is folded by a plane mirror 301 disposed between the secondoptical system 31 and the screen 4. The projector, similarly to thefirst and the second embodiment, projects light beams upward from aposition on a level below the center of the screen 4. The thirdembodiment is a typical example of application of an oblique-incidenceimaging optical system according to the present invention to aprojector. The projector is simple in construction and has asatisfactory ability as a projecting system. The distance S2 between thesecond optical system 31 and the screen 4 is 450 mm. The cone angle oflight beams received by the first optical system from the image-formingdevice 2 is 14.4° (f number of 4). In a section shown in FIG. 6, theangle between a light beam 328 extending at the largest field angle andthe reference axis 3A is 63° (the maximum angle among those between allthe light beams not included in the paper and the reference axis 3A is64.7°). Although the field angle is thus very large, distortion is assmall as 0.03%. The difference between the distance D1 along a lightbeam 321 between the first optical system 30 and the second opticalsystem 31 and the distance D2 along the same light beam 321 between thesecond optical system 31 and the screen 4 is the smallest. The distanceD1=298.2 and the distance D2=520.7, which meets the condition expressedby D2>D1.

[0133]FIG. 7 shows converging points in light beam sections. The ratioof converging points beyond the screen 4 to the converging points on acurve 31T is larger than those in the foregoing embodiments. A lightbeam 315 and those on the outer side of the same have their convergingpoints beyond the screen 4. A light beam 318 does not have anyconverging point and is a substantially parallel beam converging atinfinity. In the first and the second embodiment, converging points (Δ)have converging points in the direction of travel of light beams alongthe reference axis of the first optical system. As obvious from Table 3,in this embodiment, the converging point of a light beam relating to L1n is at a negative distance and the light beam is divergent.

[0134]FIG. 8 is a sectional view of the first optical system. In thisembodiment, the image-forming device 2 is a reflection liquid crystaldisplay. Generally, a reflection liquid crystal display needs asufficient back focal distance to secure a space for illuminating light.In this embodiment, a sufficient space is secured between theimage-forming device 2 and an optical element of the first opticalsystem 30 the nearest to the image-forming device 2, which is greaterthan eight times the focal length of the composite optical system. Thefirst optical system has a focal length f1=35.5 mm, the second opticalsystem has a focal length f2=−96 mm and the composite optical systemconsisting of the first and the second optical system has a focal lengthf=7.9 mm. Thus, the focal length f of the composite optical system isvery small as compared with the respective foci f1 and f2 of the firstand the second optical systems.

[0135] This embodiment is a first example satisfying the followingadditional conditions.

S 1/L 11>0.6

(S 1+S 2)/L 2 n<1

ΔSL>0.6

[0136] Actually, as shown in Table 4,

S 1/L 11=0.69

(S 1+S 2)/L 2 n=0.95

ΔSL=0.87

[0137] Thus, this embodiment satisfies all the foregoing conditions.When light beams fall on the screen at a large angle of incidence as inthis embodiment, severer conditions must be satisfied in addition tosatisfying the ordinary conditions to balance imaging characteristics.The aforesaid first condition signifies bringing the remotest convergingpoint of a light beam emerging from a part the nearest to the referenceaxis of the first optical system close to the second optical system. Thesecond condition signifies that alight beam emerging from a part theremotest from the reference axis of the first optical system convergeson a converging point lying beyond the conjugate plane B. The lastcondition relates to the longest converging points of a light beamemerging from a part the nearest to the reference axis of the firstoptical system and a light beam emerging from a part the remotest fromthe reference axis of the first optical system and signifies spacing therespective converging points of the light beam emerging from a part thenearest to the reference axis of the first optical system and the lightbeam emerging from a part the remotest from the reference axis of thefirst optical system a distance greater than a predetermined distanceapart from each other. Desirably, the components of the optical systemsfor realizing a large oblique angle of incidence have construction andshapes meeting at least one of those conditions. Preferred embodimentswhich will be described hereinafter meet at least one of the threeaforesaid conditions.

[0138]FIG. 9 is a sectional view of a front projector in a fourthembodiment according to the present invention similar to those in theforegoing embodiments. This front projector differs from the foregoingprojectors in that the projector is disposed just beside a screen 4, andthe position of an image on the screen 4 can be moved. FIG. 9 is asectional view taken on a horizontal plane dividing the screen 4 intoequal upper and lower halves. FIG. 10 is a front view of the frontprojector shown in FIG. 9.

[0139] An image-forming device 2 is a 0.7 in. reflection image-formingdevice. Light beams emitted by the image-forming device 2 travel througha first optical system 30 including refracting optical elements and asecond optical system 31 including a single reflecting mirror and form a60 in. image on a screen 4. The image formed on the screen 4 can bemoved horizontally. A 60 in. image formed in a region between lightbeams 321 and 328 can be laterally moved a distance equal to half thewidth of the screen 4 to a region between light beams 321′ and 328′,which makes a viewer have an illusion that the screen 4 indicated bycontinuous lines in FIG. 10 moves to a position indicated by dottedlines 4′ in FIG. 10. The projector capable of obliquely projecting animage on the screen through a short distance of projection rarelyhinders viewer's viewing the image formed on the screen; a function tomove an image horizontally is important for increasing the degree offreedom of installation of the projector.

[0140]FIG. 11 shows the converging points of light beams emerging fromthe first optical system 30 in the same section as that shown in FIG.10. Light beams emerging from the first optical system 30 are reflectedby the second optical system 31 and converge on the screen 4. In FIG.11, light beams are not reflected by the second optical system 31 andare traveling through the second optical system 31 toward positionscorresponding to those on the screen 4. The distance S2 between thesecond optical system 31 and the screen 4 is 700 mm. Points marked witha blank triangle (Δ) are converging points on the paper, and pointsmarked with a solid circle () are on a light beam section perpendicularto the paper. As obvious from FIG. 11, a light beam emerging from a partof the first optical system 30 farther from the reference axis 3Aconverges on a converging point farther from the first optical system30, and a light beam 318′ is a divergent light beam that does notconverge. The light beams farther from the reference axis 3A havesmaller converging angles. The light beam 318′ has a negative convergingangle. The converging points marked with a solid circle () in thesection perpendicular to the sheet are nearer to the first opticalsystem 30 than those marked with a blank triangle (Δ). The light beam318′ has a converging point substantially on the screen. The cone angleof the light beams received from the image-forming device 2 by the firstoptical system 30 is 14.4° (f number of 4) and a maximum distortion is0.23%. FIG. 12 is a sectional view of the first optical system 30.

[0141]FIG. 13 shows a rear projector in a fifth embodiment according tothe present invention. The rear projector projects an image on a screenfrom behind the screen and a viewer views the image from the front sideof the screen similarly to viewing an image on an ordinary televisionscreen.

[0142] An image-forming device 2 included in a conjugate plane A is atransmission liquid crystal display. Light beams emitted by theimage-forming device 2 are reflected by two reflecting mirrors 30 a and30 b included in a first optical system, a single reflecting mirror 31included in a second optical system, and a plane mirror 301 to form anenlarged image on a screen 4 included in the other conjugate plane B.The image-forming device 2 is provided with a 1.3 in. screen. A 50 in.image is formed on the screen 4. Since the light beams are thus foldedback by the plane mirror 301, the rear projector can be formed in asmall thickness. The distance between the plane mirror 301 and thescreen 4 is 280 mm (S2=520 mm). The thickness of the rear projector isabout half that of the corresponding conventional rear projector. FIG.14 is a rear view of the rear projector. FIG. 15 shows the convergingmode of light beams, and FIG. 16 shows an enlarged view of an imagingsystem. The cone angle of the light beams received by the first opticalsystem 30 from the image-forming device 2 is 11.5° (f number is 5), anda maximum distortion is 0.57%.

[0143]FIG. 17 is a sectional view of a rear projector in a sixthembodiment according to the present invention, and the sixth embodimentis related to the rear projector as well as the fifth embodiment andFIG. 17 is a top view of the rear projector of the sixth embodiment.

[0144] Light beams emitted by a 0.7 in. image-forming device 2 travelthrough a first optical system 30 including refracting optical elements,a plane mirror 301, a second optical system 31 including a singlereflecting mirror, and a plane mirror 302, and fall on a screen 4 toform a 100 in. image. The rear projector has a small thickness. Thedistance between the plane mirror 302 and the screen 4 is 400 mm. Theheight of the lower end of the screen 4 from the first optical system 30disposed in a lower part of the rear projector is small and the rearprojector has a small overall height. The cone angle of light beamsreceived by the first optical system 30 from the image-forming device 2is 23.1° (f number is 2.5) and distortion is 0.06% or below. FIG. 18 isa front elevation of the rear projector, and FIG. 19 is a sectional viewof the first optical system 30.

[0145]FIG. 20 is a sectional view of a projector in a seventh embodimentaccording to the present invention. An image-forming device 2 isprovided with a 0.7 in. screen having an aspect ratio of 16:9. Lightbeams emitted by the image-forming device 2 travel through a firstoptical system 30 including refracting optical elements, and a secondoptical system 31 including a single reflecting mirror, and fall on ascreen 4. It is a feature of this embodiment that the difference betweenthe incidence angle of the light beam falling on the lower end of thescreen 4 and that of the light beam falling on the upper end of thescreen 4 is small. More concretely, the incidence angle of the lightbeam on the lower end of the screen 4 is 63°, the incidence angle of thelight beam on the upper end of the screen 4 is 77°, and hence thedifference is 14°. The distance of projection is short. The distance S2between the reference axis 3B of the second optical system 31 and thescreen 4 is 167 mm, and the distance S1 between the first optical system30 and the second optical system 31 is 300 mm, which is longer than thedistance S2. When applying the projector to a practical use, theprojector may be additionally provided with a plane mirror to fold theoptical path of the projector. Although Si>S2, the distances D1 and D2along a light beam 321 meet a condition: D1<D2. FIG. 21 is a sectionalview of the first optical system 30. The cone angle of the light beamsreceived by the first optical system 30 from the image-forming device 2is 23° (f number is 2.5).

[0146]FIG. 22 shows a rear projector in an eighth embodiment accordingto the present invention similar to the rear projector in the fifthembodiment. This rear projector has first and second optical systemscomprising only reflecting mirrors. This rear projector differs fromthat in the fifth embodiment in that the first optical system includesthree reflecting mirrors 30 a, 30 b and 30 c, and the second opticalsystem includes a single reflecting mirror. An image produced by a 0.7in. image-forming device 2 is projected in an enlarged 40 in. image on ascreen 4. All the reflecting mirrors have rotationally symmetricaspheric surfaces having axis of rotation symmetry, respectively. Allthe reflecting mirrors are decentered and do not have any common opticalaxis. A reference axis 3A is supported to be an expedient commonreference axis of the first and the second optical systems for definingthe degrees of decentering of the reflecting mirrors. This axis has nophysical significance and is an entirely expedient axis. The cone angleof light beams received by the first optical system from theimage-forming device 2 is 16.4° (f number is 3.5), which enables theprojection of a sufficiently bright image on the screen 4. The distancebetween the plane mirror 301 and the screen 4, i.e., the thickness ofthe rear projector, is 160 mm.

[0147]FIG. 23 is a sectional view of a rear projector in a ninthembodiment according to the present invention. Although basically thesame in construction as the rear projector in the eighth embodiment,this rear projector in the ninth embodiment has a first optical system30 including three reflecting mirrors respectively having free-formsurfaces. Although the rear projector is capable of projecting lightbeams on a screen 4 to form a 40 in. image, the distance between a planemirror 301 and the screen 4 is only 125 mm, which is only 25% of adiagonal. Although various defining equations can be applied to definethe free-form surfaces, this embodiment employs Zernike's polynomials.The component optical elements are decentered greatly. A thirdreflecting mirror 30 c of the first optical system 30 has an angle ofrotational decentering of about 35°. A paraxial way of thinking cannotbe applied any more to this optical system, which is apparent from thefocal length f1 of 5.49 mm of the first optical system and the focallength f of −1.34 mm of the entire system calculated on the basis ofparaxial values. In the vicinity of a reference axis, the first opticalsystem is a converging system and the second optical system is adiverging system. The cone angle of light beams received by the firstoptical system from an image-forming device 2 is 14.4° (f number is 4).

[0148] The projectors in preferred embodiments have been described. Itis important to constitute an oblique-incidence imaging systemregardless of the components of the concrete optical systems of therefracting and reflecting system by satisfying the basic conditions,which expands the range of selection of concrete means for realizing anoblique-incidence optical system according to the level of availabletechniques and manufacturing costs.

[0149] Numerical values relating to the foregoing embodiments will begiven.

[0150] Table 7 shows numerical values for the first embodiment by way ofexample. In Table 7, numbers 1 to 14 correspond to reference numerals 1to 14 in FIG. 3 showing the first optical system 30, respectively.Refractive indices and variances correspond to values for the surfaces,respectively. A number 0 indicates the image-forming device 2, and d0 isthe distance along the optical axis between the image-forming device 2and the first surface 41 of the first optical system. TABLE 7 Radius Rof Refractive Variance Number curvature Interval d index n vd 0 0.0046.89 1.00000 1 132.14 8.80 1.61272 58.60 2 −75.09 0.10 1.00000 3 60.2118.00 1.61272 58.60 4 −117.38 1.50 1.71736 29.50 *5 46.92 50.63 1.000006 163.32 1.50 1.68893 31.20 7 46.29 12.00 1.61272 58.60 8 −110.33 27.711.00000 9 278.19 12.00 1.61272 58.60 10 −86.98 0.10 1.00000 11 64.2534.19 1.69700 48.50 12 38.97 15.10 1.00000 13 −31.77 3.00 1.64048 59.75*14 422.41 280.00 1.00000 *15 401.49 −2000.00 MIRROR 16 0.00 0.001.00000

[0151] In Table 7, surfaces indicated at numbers with asterisk (*) areaspherical surfaces. In the first to the eighth embodiment, theaspherical surfaces are defined by the following expression. Althoughthe aspherical surfaces may be defined by other expressions, thefollowing expression is employed only because the same is usedprevalently.$z = {\frac{{ch}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}h^{2}}}} + {A_{4}h^{4}} + {A_{6}h^{6}} + {A_{8}h^{8}} + \ldots + {A_{26}h^{26}}}$

[0152] where z is a depth along the optical axis from a reference planeincluding the apex of each aspherical surface, c is the reciprocal ofthe radius R of curvature, h is the distance of a point on the surfacefrom the optical axis, k is conic constant and A₄ to A₂₆ are asphericalsurface correction coefficients which are tabulated in Table 8. TABLE 8Aspherical Aspherical Aspherical Degree surface 5 surface 14 surface 15K 0.439 248.749 −7.2690E+00 A4    1.3862E−06   7.4830E−07 −1.6430E−08A6    3.0821E−10 −3.2900E−09   5.1019E−13 A8  −1.0760E−11   1.5662E−11−8.4150E−18 A10   6.9165E−14 −6.2460E−14   3.6849E−23 A12   1.0057E−16  1.3482E−16 −1.7400E−28 A14 −1.2250E−18 −1.1350E−19   5.3673E−33 A16−9.6450E−22 −2.1580E−22 −3.2500E−38 A18   9.6730E−24   6.7512E−25  1.3007E−42 A20   2.4747E−26 −1.2460E−28   1.1514E−45 A22 −1.0400E−28−3.7560E−31 −3.6110E−51 A24 −9.1410E−33 −4.0710E−33 −1.6490E−55 A26  1.7644E−34   6.5807E−36 −2.0690E−59

[0153] In Table 7, a surface No. 15 is a reflecting surface of thesecond optical system 31. This surface also is an aspherical surfaceexpressed by the foregoing expression. In FIG. 3, d14 is the distancealong the optical axis between a surface r14 of the first optical systemand the second optical system 31, and d15 is the distance along theoptical axis between the second optical system and the screen 4. Thenumber 16 indicates the screen 4.

[0154] Numerical values relating to the second embodiment are tabulatedin tables 9 and 10. TABLE 9 Radius R of Refractive Variance Numbercurvature Interval d index n vd 0 0.00 0.00 1.00000 1 0.00 32.44 1.5168064.20 2 0.00 104.17 1.00000 *3 114.85 20.00 1.58913 61.30 *4 −112.32237.00 1.00000 *5 −97.19 10.00 1.51680 64.20 *6 −543.21 300.00 1.00000*7 −170.55 15.00 1.51680 64.20 *8 127.52 700.00 1.00000 9 0.00 0.001.00000

[0155] TABLE 10 Aspherical Aspherical Aspherical Aspherical AsphericalAspherical Degree surface 3 surface 4 surface 5 surface 6 surface 7surface 8 K −0.967 −3.427 −0.961 38.098 −4.661 −137.657 A4  −4.7621E−08−2.1521E−08 −3.9210E−07 −4.6976E−09 −1.9806E−07 −3.2553E−08 A6 −1.1887E−13 −4.3560E−12   6.2030E−12 −1.2979E−12   1.0092E−11  3.6760E−13 A8  −1.9196E−15   2.4159E−15 −2.0548E−15 −2.7614E−15−5.3323E−16 −2.1936E−18 A10 −1.6656E−19 −8.8558E−19 −6.7797E−18  3.3560E−19   8.8135E−21   5.1099E−24

[0156] Numbers 3 and 4 correspond to data on the surface of a convexlens on the side of the image-forming device 2 of the first opticalsystem 30 shown in FIG. 4, and numbers 5 and 6 correspond to data on thesurface of a concave lens on the side of the screen of the same firstoptical system 30. Numbers 7 and 8 correspond to data on the surface ofthe optical element included in the second optical system 31. A number 0correspond to the image-forming device 2, a number 9 corresponds to thescreen 4, and numbers 1 and 2 correspond to color-synthesizing prisms.

[0157] Numerical values relating to the third embodiment are tabulatedin tables 11 and 12. Numbers 1 to 11 correspond to r1 to r11 shown inFIG. 8, respectively, and numbers 0, 12, 13 and 14 correspond to theimage-forming device 2, the folding plane mirror, the aspherical mirror31 included in the second optical system and the screen, respectively.TABLE 11 Radius R of Refractive Variance Number curvature Interval dindex n vd 0 0.00 64.00 1 58.19 11.00 1.60300 65.50 2 −273.18 32.30 *375.74 9.00 1.60300 65.50 4 −33.90 1.80 1.74000 31.70 5 228.46 67.00 61929.73 6.00 1.80400 46.60 7 −78.35 18.60 8 53.10 24.00 1.60311 60.70 934.61 15.80 *10 −22.93 3.00 1.60311 60.70 11 −83.73 100.00 12 0.00−200.00 MIRROR *13 −191.80 −450.00 MIRROR 14 0.00 0.00

[0158] TABLE 12 Aspherical Aspherical Aspherical Degree surface 3surface 10 surface 13 K −2.578 −0.228 −7.226 A4  −1.0273E−06  1.5697E−06   4.5923E−09 A6  −6.6235E−10 −2.2420E−09 −7.5917E−14 A8 −7.2979E−13   2.3452E−11   8.6846E−19 A10 −6.8308E−15 −4.6973E−14−5.1711E−24 A12   4.2929E−17   3.5456E−18 −1.6600E−30 A14 −1.0068E−19  1.7720E−19   1.9636E−34 A16   7.3009E−23 −2.0286E−22 −7.4399E−40

[0159] Numerical values relating to the fourth embodiment are tabulatedin tables 13 and 14. Numbers 1 to 13 correspond to r1 to r13 shown inFIG. 12, respectively. Reference character r14 indicates data on thesurface of the reflecting surface 31 of the second optical system. Thisoptical system corrects aberration for a wider range of image height todeal with the movement of the image. Numbers 0 and 15 correspond to theimage-forming device 2 the screen, respectively. TABLE 13 Radius R ofRefractive Variance Number curvature Interval d index n vd 0 0.00 61.241.00000 1 51.50 14.00 1.62000 62.20 2 8402.87 29.53 1.00000 *3 76.3111.00 1.62000 62.20 4 −30.99 2.00 1.74000 31.70 5 237.26 61.38 1.00000 6358.55 16.40 1.69350 53.30 7 −68.17 5.23 1.00000 8 59.70 22.00 1.6131044.40 9 2509.25 1.70 1.00000 10 −254.23 3.00 1.53256 45.90 11 38.5716.99 1.00000 *12 −26.00 3.00 1.62000 62.20 13 −139.86 300.00 1.00000*14 205.53 −700.00 MIRROR 15 0.00 0.00 1.00000

[0160] TABLE 14 Aspherical Aspherical Asphe-rical Degree surface 3surface 12 surface 14 K −6.351 −0.088 −7.181 A4  −4.5222E−07  9.8683E−07 −5.1802E−09 A6  −1.3212E−09 −1.4119E−09   9.4568E−14 A8 −8.3071E−13   1.9531E−11 −1.1176E−18 A10 −4.8053E−15 −3.9940E−14  6.5972E−24 A12   3.2936E−17   2.8893E−17   3.3104E−31 A14 −8.1805E−20  3.8128E−20 −2.0325E−34 A16   7.4349E−23 −3.7771E−23   7.1276E−40

[0161] Numerical values relating to the fifth embodiment are tabulatedin tables 15 and 16.

[0162] This is a numerical example of a rear projector having an imagingsystem including only reflecting mirrors. Numbers 3 and 4 in Table 15are surface data corresponding to the reflecting mirrors 30 a and 30 bshown in FIG. 16, respectively. A number 5 in Table 15 corresponds tosurface data on the reflecting mirror 31 of the second optical system31. Surface data 0 is the image-forming device 2, surface data 6 is theplane reflecting mirror 301, and surface numbers 1 and 2 arecolor-synthesizing prisms. TABLE 15 Radius R of Refractive VarianceNumber curvature Interval d index n vd 0 0.00 1.00000 1 0.00 32.441.51680 64.20 2 0.00 142.35 1.00000 *3 −224.00 −250.00 MIRROR *4 −306.02230.00 MIRROR *5 207.25 −240.00 MIRROR 6 0.00 280.00 MIRROR 7 0.00 0.001.00000

[0163] TABLE 16 Aspherical Aspherical Aspherical Degree surface 3surface 4 surface 5 K −0.069 16.832 −10.626 A4    1.2148E−10 −1.0440E−07−4.6180E−09 A6  −1.2979E−12   1.6437E−11   5.7203E−14 A8  −6.9055E−17  5.9316E−15 −4.1342E−19 A10   8.8408E−20 −1.2979E−18   1.2506E−24

[0164] Numerical values relating to the sixth embodiment are tabulatedin tables 17 and 18. Numbers 1 to 14 correspond to r1 to r14 of thefirst optical system shown in FIG. 19, respectively, and numbers 15, 16and 17 correspond to the plane mirror for 90°-folding, the asphericalreflecting mirror 31 of the second optical system and the foldingreflecting mirror 301, respectively. A number 0 and 18 corresponds tothe image-forming device 2 and the screen 4, respectively. TABLE 17Radius R of Refractive Variance Number curvature Interval d index n vd 00.00 45.62 1.00000 1 118.08 8.80 1.56883 56.00 2 −71.33 0.10 1.00000 354.78 18.00 1.56883 56.00 4 −98.49 1.50 1.71736 29.50 *5 57.02 28.051.00000 6 216.13 1.50 1.68893 31.20 7 45.58 12.00 1.56883 56.00 8−112.64 55.48 1.00000 9 254.11 12.00 1.56883 56.00 10 −88.77 0.101.00000 11 55.71 34.13 1.69700 48.50 12 31.90 14.44 1.00000 13 −27.543.00 1.64048 59.75 *14 −233.03 80.00 1.00000 15 0.00 −200.00 MIRROR *16−162.77 350.00 MIRROR 17 0.00 −400.00 MIRROR 18 0.00 0.00 1.00000

[0165] TABLE 18 Aspherical Aspherical Aspherical Degree surface 5surface 14 surface 16 K  0.419  8.885 −6.765 A4    1.7575E−06  4.0485E−07   5.1924E−09 A6    3.5104E−09 −1.1450E−09 −8.1620E−14 A8 −3.5400E−11   1.0964E−11   8.1952E−19 A10   1.5737E−13 −5.9200E−14−4.0570E−24 A12 −1.4420E−17   1.5071E−16   8.0087E−30 A14 −1.3420E−18−1.1300E−19 −1.8850E−34 A16 −5.2260E−22 −2.5080E−22   2.0596E−39 A18  1.2545E−23   5.6635E−25   1.7805E−45 A20   1.3186E−27 −2.9910E−28  1.2608E−50 A22 −2.1590E−29 −5.5790E−32 −7.9730E−55 A24 −1.9490E−31−2.8470E−35 −5.7130E−60 A26   3.7569E−34   7.8403E−38  6.6673E−65

[0166] Numerical values relating to the seventh embodiment are tabulatedin tables 19 and 20. Numbers 1 to 17 correspond to r1 to r17 of thefirst optical system shown in FIG. 21, respectively. A number 18corresponds to the aspherical reflecting mirror of the second opticalsystem. A number 0 and 19 correspond to the image-forming device 2 andthe screen 4, respectively. Although a color-synthesizing prism isdisposed adjacently to the image-forming device as shown in FIG. 21, thecolor-synthesizing prism is represented by air-equivalent length. TABLE19 Radius R of Refractive Variance Number curvature Interval d index nvd 0 0.00 57.60 1.00000 *1 42.02 13.34 1.49180 57.40 2 −95.32 0.201.00000 3 79.94 10.25 1.60300 65.50 4 −101.91 0.20 1.00000 5 −413.352.00 2.00330 28.27 6 34.87 10.37 1.60300 65.50 7 −1899.87 0.20 1.00000 847.31 7.07 1.80810 22.80 9 216.68 0.20 1.00000 10 35.36 2.00 1.4874970.20 *11 19.06 70.22 1.00000 12 359.84 8.71 2.00330 28.27 13 −61.993.80 1.00000 *14 −45.75 2.64 1.63930 44.90 15 62.36 15.25 1.00000 *16−40.00 3.50 1.49180 57.40 *17 −45.29 300.00 1.00000 *18 41.50 −167.00MIRROR 0 0

[0167] TABLE 20 De- Aspherical Aspherical Aspherical Aspherical greesurface 1 surface 11 surface 17 surface 18 K −1.39512 −0.69407  1.22499−3.55242 A4  −4.3850E−06   6.1477E−06   1.9389E−06 −1.2694E−08 A6   1.4582E−09 −1.5904E−09   2.5985E−10   3.1819E−13 A8  −2.2531E−13  2.9926E−11 −4.4379E−13 −3.1329E−18 A10 −8.5179E−17 −5.9717E−14  1.5357E−15 −8.2909E−23 A12   3.3215E−27 A14 −4.0876E−32 A16  2.5544E−38 A18   3.5555E−38 A20 −2.2263E−47

[0168] Numerical values relating to the eighth embodiment are tabulatedin tables 21, 22 and 23. Numbers 3, 4 and 5 in Table 21 correspond todata on the surfaces of the reflecting mirrors 30 a, 30 b and 30 c ofthe first optical system shown in FIG. 22, respectively. A number 6 inTable 21 corresponds to data on the surface of the reflecting mirror 31of the second optical system 31. A number 8 corresponds to the screen 4,and numbers 1 and 2 corresponds to covering glass plates. Decenteringdistances for the reflecting mirrors are tabulated in Table 23.Y-decentering signifies upward decentering (positive decentering) in thepaper, and x-axis rotation signifies clockwise rotation (rotation in thepositive direction) in the paper. TABLE 21 Radius R of RefractiveVariance Number curvature Interval d index n vd 0 0.00 0.00 1.00000 *10.00 3.00 1.48749 70.20 2 0.00 47.45 1.00000 *3 −58.87 −44.01 MIRROR *4−58.04 55.95 MIRROR *5 −275.83 −97.16 MIRROR *6 −67.60 97.16 MIRROR 70.00 −160.00 MIRROR 8 0.00 0.00 1.00000

[0169] TABLE 22 De- Aspherical Aspherical Aspherical Aspherical greesurface 3 surface 4 surface 5 surface 6 K −0.4777 −3.7602  0.0000−5.9287 A4  −3.1048E−07 −6.8743E−06   3.5717E−07   4.8051E−08 A6 −2.3345E−10 −3.9861E−09 −7.7774E−11 −2.8630E−12 A8    2.1957E−13−6.3211E−11   1.0188E−14   1.1106E−16 A10 −1.2237E−16   4.0709E−13−7.3354E−19 −2.7008E−21 A12 −8.2854E−20 −1.0604E−15   2.1842E−23  3.7047E−26 A14 −2.1837E−31

[0170] TABLE 23 Y- X-axis Number decentering rotation 3 0.69 4 0.74−0.04 5 2.24 −0.20 6 2.16 0.05

[0171] Numerical values relating to the ninth embodiment are tabulatedin tables 24, 25, 26 and 27. Basic explanation of those numerical valuestabulated in Tables 24, 25 and 26 is the same as that of the numericalvalues relating to the eighth embodiment. Coefficients for extendingaspherical surfaces to free-form surfaces are tabulated in Table 27.Those coefficients are for additional Zernike's polynomials forexpressing free-form surfaces in addition to the aspherical surfaces.The selection of those, similarly to the selection of the definingequation for defining the aspherical surfaces, is expedient, and otherdefining equation may be used. Polynomials corresponding to thecoefficients are given below Table 27. TABLE 24 Radius R of RefractiveVariance Number curvature Interval d index n vd 0 0.00 0.00 1.00000 10.00 3.00 1.48749 70.20 2 0.00 111.89 1.00000 *3 −99.09 −61.35 MIRROR *4−150.67 65.88 MIRROR *5 −17.28 −80.26 MIRROR *6 −45.42 80.26 MIRROR 70.00 −125.00 MIRROR 8 0.00 0.00 1.00000

[0172] TABLE 25 De- Aspherical Aspherical Aspherical Aspherical greesurface 3 surface 4 surface 5 surface 6 K 3.0923 11.8991 −1.2208 −7.1652A4    5.2959E−07   1.4526E−06   3.3385E−06   1.2521E−07 A6    1.9358E−10  3.0479E−09 −6.419E−10 −1.4744E−11 A8  −9.1311E−15 −1.2760E−13  1.5704E−13   1.1538E−15 A10   2.9509E−17   6.4874E−17 −1.2058E−17−5.6704E−20 A12   1.5663E−24 A14 −1.8473E−29

[0173] TABLE 26 Y- X-axis Number decentering rotation 3 −1.78 4 −13.0724.43 5 9.85 −34.91 6 27.80 −3.35

[0174] TABLE 27 Degree Zernike 3 Zernike 4 Zernike 5 1 2 3   2.2803E−02−2.7053E−01 −1.8405E−01 4   1.8972E−04   8.3429E−04   1.6732E−02 5 6−8.1097E−05 −7.7138E−04 −6.1242E−03 7 −5.6180E−07 −4.4644E−06−1.4254E−04 8 9   4.0821E−08 −2.8891E−06   2.2379E−05 10 11 −8.9052E−09−1.1475E−07   2.8221E−07 12   1.7020E−10   3.3320E−08 −5.2899E−07 13 14−1.7338E−10   6.0622E−09 −1.5702E−07 15 16 17 −9.5911E−12   5.7540E−10  8.4471E−10 18 19   1.0418E−11   1.7730E−10   1.0706E−09 20 21−1.8783E−11 −1.1520E−11   2.2288E−09 22 −1.0294E−12 −6.3528E−11−1.0883E−11 23 24 −2.7047E−13 −5.7456E−12   5.4642E−12 25 26 −2.8390E−13−4.4963E−13   2.6375E−12

[0175] Expressions of only terms which are not zero in Table 27 amongZernike's additive terms are enumerated below. Numerals on the left sideof the expressions correspond to the degrees tabulated in Table 27.

3

{square root}{square root over (4)}ρ sin φ

4

{square root}{square root over (3)}(2ρ²−1)

6

{square root}{square root over (6)}ρ² cos 2φ

7

{square root}{square root over (8)}(3ρ³−2ρ)sin φ

9

{square root}{square root over (8)}ρ³ sin 3φ

11

{square root}{square root over (5)}(6ρ⁴−6ρ+1)

12

{square root}{square root over (10)}(4ρ⁴−3ρ²)cos 2φ

14

{square root}{square root over (10)}ρ⁴ cos 4φ

17

{square root}{square root over (12)}(10ρ⁵−12ρ³+3ρ)sin φ

19

{square root}{square root over (12)}(5ρ⁵−4ρ³)sin 3φ

21

{square root}{square root over (12)}ρ⁵ sin 5φ

22

{square root}{square root over (7)}(20ρ⁶−30ρ⁴+12ρ²−1)

24

{square root}{square root over (14)}(15ρ⁶−20ρ⁴+6ρ²)cos 2φ

26

{square root}{square root over (14)}(6υ⁶−5ρ⁴)cos 4φ

28

{square root}{square root over (14)}ρ⁶ cos 6φ

[0176] Numerical data relating to the foregoing embodiments are givenabove. Although the second optical system of each of the foregoingembodiments includes the single reflecting mirror or the singlerefracting element, the second optical system causes various problems inmanufacture and costs if the second optical system comprises a pluralityof optical elements because the second optical system is comparativelylarge. Therefore, the second optical system of each of the foregoingembodiments comprises the single optical element. The degree of freedomcan be increased if the second optical system comprises a plurality ofoptical elements. All the second optical systems of the foregoingembodiments include rotationally symmetric elements for the same reason.The use of optical element having a free-form surface increases thedegree of freedom of design.

INDUSTRIAL APPLICABILITY

[0177] The present invention is applicable to the field ofoblique-incidence imaging optical systems, particularly, fields of realimage formation, such as the fields of projectors, image readers andcameras, and the present invention realizes an oblique-incidence imagingoptical system having a half-field angle exceeding 60°.

1-10. (canceled)
 11. An image optical system in which a plurality oflight beams emerging from an image-forming device on a conjugate plane Aand having a divergence angle of 10° or greater is made obliquelyincident upon a conjugate plane B to form on the conjugate plane B anenlarged image approximately similar to an image formed by theimage-forming device, said image optical system comprising: a firstoptical system and a second optical system, the first optical systemincluding a plurality of refracting optical elements having a commonoptical axis and having the function of converging the plurality oflight beams emerging from the image-forming device on both of a firstlight beam cross section parallel to principal rays and a second lightbeam cross section intersecting the first light beam cross section, thesecond optical system including a reflecting optical element having afree-form surface and having the function of converging light beamspassing through the first optical system on the conjugate plane B, thefirst optical system having a first reference axis passing through aposition nearer to a light beam traveling through the shortest opticalpath from the conjugate plane A to the conjugate plane B than to a lightbeam traveling through the longest optical path from the conjugate planeA to the conjugate plane B, the first reference axis being perpendicularto the conjugate plane A, the second optical system having a secondreference axis passing through a position nearer to a light beamtraveling through the shortest optical path from the conjugate plane Ato the conjugate plane B than to a light beam traveling through thelongest optical path from the conjugate plane A to the conjugate planeB, the second reference axis being perpendicular to the conjugate planeB, wherein if the distance from the point of emergence on the firstoptical system to the point of incidence on the second optical systemalong the first reference axis is S1 and the distance from the point ofemergence on the second optical system to the conjugate plane B alongthe second reference axis is S2; if the maximum and minimum of thedistance between a point of convergence in the first and second lightbeam cross sections of a light beam emerging from the first opticalsystem at a point nearest to the first reference axis and the point ofemergence on the first optical system are L11 and L21, respectively; ifthe maximum and minimum of the distance between the point of convergencein the first and second light beam cross sections of a light beamemerging from the first optical system at a point remotest from thefirst reference axis and the point of emergence on the first opticalsystem are L1 n and L2 n, conditions expressed by S 1≦L 11≦S 1+S 2 S 1≦L21≦S 1+S 2 L 11/L 1 n<0.250<L 21/L 2 n<1.5 are satisfied.
 12. An imageoptical system in which a plurality of light beams emerging from animage-forming device on a conjugate plane A and having a divergenceangle of 10° or greater is made obliquely incident upon a conjugateplane B to form on the conjugate plane B an enlarged image approximatelysimilar to an image formed by the image-forming device, said imageoptical system comprising: a first optical system and a second opticalsystem, the first optical system including a plurality of refractingoptical elements having a common optical axis and having the function ofconverging the plurality of light beams emerging from the image-formingdevice on both of a first light beam cross section parallel to principalrays and a second light beam cross section intersecting the first lightbeam cross section, the second optical system including a reflectingoptical element having a free-form surface and having the function ofconverging light beams passing through the first optical system on theconjugate plane B, the first optical system having a first referenceaxis passing through a position nearer to a light beam traveling throughthe shortest optical path from the conjugate plane A to the conjugateplane B than to a light beam traveling through the longest optical pathfrom the conjugate plane A to the conjugate plane B, the first referenceaxis being perpendicular to the conjugate plane A, the second opticalsystem having a second reference axis passing through a position nearerto a light beam traveling through the shortest optical path from theconjugate plane A to the conjugate plane B than to a light beamtraveling through the longest optical path from the conjugate plane A tothe conjugate plane B, the second reference axis being perpendicular tothe conjugate plane B, wherein if the distance from the point ofemergence on the first optical system to the point of incidence on thesecond optical system along the first reference axis is S1 and thedistance from the point of emergence on the second optical system to theconjugate plane B along the second reference axis is S2; if the maximumand minimum of the distance between a point of convergence in the firstand second light beam cross sections of a light beam emerging from thefirst optical system at a point nearest to the first reference axis andthe point of emergence on the first optical system are L11 and L21,respectively; if the maximum and minimum of the distance between thepoint of convergence in the first and second light beam cross sectionsof a light beam emerging from the first optical system at a pointremotest from the first reference axis and the point of emergence on thefirst optical system are L1 n and L2 n, respectively; if the distancealong an arbitrary light beam from the first optical system to thesecond optical system is D1 and the distance along the arbitrary lightbeam from the second optical system to the conjugate plane B is D2,conditions expressed by S 1≦L 11≦S 1+S 2 S 1≦L 21≦S 1+S 2 L 11/L 1n<0.250<L 21/L 2 n<1.5D1≦D2 are satisfied.
 13. An image optical systemin which a plurality of light beams emerging from an image-formingdevice on a conjugate plane A and having a divergence angle of 10° orgreater is made obliquely incident upon a conjugate plane B to form onthe conjugate plane B an enlarged image approximately similar to animage formed by the image-forming device, said image optical systemcomprising: a first optical system and a second optical system, thefirst optical system including a plurality of refracting opticalelements having a common optical axis and having the function ofconverging the plurality of light beams emerging from the image-formingdevice on both of a first light beam cross section parallel to principalrays and a second light beam cross section intersecting the first lightbeam cross section, the second optical system including a reflectingoptical element having a free-form surface and having the function ofconverging light beams passing through the first optical system on theconjugate plane B, the first optical system having a first referenceaxis passing through a position nearer to a light beam traveling throughthe shortest optical path from the conjugate plane A to the conjugateplane B than to a light beam traveling through the longest optical pathfrom the conjugate plane A to the conjugate plane B, the first referenceaxis being perpendicular to the conjugate plane A, the second opticalsystem having a second reference axis passing through a position nearerto a light beam traveling through the shortest optical path from theconjugate plane A to the conjugate plane B than to a light beamtraveling through the longest optical path from the conjugate plane A tothe conjugate plane B, the second reference axis being perpendicular tothe conjugate plane B, wherein if the distance from the point ofemergence on the first optical system to the point of incidence on thesecond optical system along the first reference axis is S1 and thedistance from the point of emergence on the second optical system to theconjugate plane B along the second reference axis is S2; if the maximumand minimum of the distance between a point of convergence in the firstand second light beam cross sections of a light beam emerging from thefirst optical system at a point nearest to the first reference axis andthe point of emergence on the first optical system are L11 and L21,respectively; if the maximum and minimum of the distance between thepoint of convergence in the first and second light beam cross sectionsof a light beam emerging from the first optical system at a pointremotest from the first reference axis and the point of emergence on thefirst optical system are L1 n and L2 n, respectively; if the differencebetween the maximum and minimum of the ratio S1/L1 of the distance L1and the distance S1 is ΔSL, conditions expressed by S 1≦L 11≦S 1+S 2 S1≦L 21≦S 1+S 2 L 11/L 1 n<0.250<L 21/L 2 n<1.5 are satisfied and atleast one of conditions expressed by S 1/L 11>0.6(S 1+S 2)/L 2n<1ΔSL>0.6 is further satisfied.
 14. An image optical system in which aplurality of light beams emerging from an image-forming device on aconjugate plane A and having a divergence angle of 10° or greater ismade obliquely incident upon a conjugate plane B to form on theconjugate plane B an enlarged image approximately similar to an imageformed by the image-forming device, said image optical systemcomprising: a first optical system and a second optical system, thefirst optical system including a plurality of refracting opticalelements having a common optical axis and having the function ofconverging the plurality of light beams emerging from the image-formingdevice on both of a first light beam cross section parallel to principalrays and a second light beam cross section intersecting the first lightbeam cross section, the second optical system including a reflectingoptical element having a free-form surface and having the function ofconverging light beams passing through the first optical system on theconjugate plane B, the first optical system having a first referenceaxis passing through a position nearer to a light beam traveling throughthe shortest optical path from the conjugate plane A to the conjugateplane B than to a light beam traveling through the longest optical pathfrom the conjugate plane A to the conjugate plane B, the first referenceaxis being perpendicular to the conjugate plane A, the second opticalsystem having a second reference axis passing through a position nearerto a light beam traveling through the shortest optical path from theconjugate plane A to the conjugate plane B than to a light beamtraveling through the longest optical path from the conjugate plane A tothe conjugate plane B, the second reference axis being perpendicular tothe conjugate plane B, wherein if the distance from the point ofemergence on the first optical system to the point of incidence on thesecond optical system along the first reference axis is S1 and thedistance from the point of emergence on the second optical system to theconjugate plane B along the second reference axis is S2; if the maximumand minimum of the distance between a point of convergence in the firstand second light beam cross sections of a light beam emerging from thefirst optical system at a point nearest to the first reference axis andthe point of emergence on the first optical system are L11 and L21,respectively; if the maximum and minimum of the distance between thepoint of convergence in the first and second light beam cross sectionsof a light beam emerging from the first optical system at a pointremotest from the first reference axis and the point of emergence on thefirst optical system are L1 n and L2 n, respectively; if the distancealong an arbitrary light beam from the first optical system to thesecond optical system is D1 and the distance along the arbitrary lightbeam from the second optical system to the conjugate plane B is D2; andif the difference between the maximum and minimum of the ratio S1/L1 ofthe distance L1 and the distance S1 is ΔSL, conditions expressed by S1≦L 11≦S 1+S 2 S 1≦L 21≦S 1+S 2 L 11/L 1 n<0.250<L 21/L 2 n<1.5D1<D2 aresatisfied and at least one of conditions expressed by S 1/L 11>0.6(S 1+S2)/L 2 n<1ΔSL>0.6 is further satisfied.